https://www.desmos.com/calculator/qbgimkc2hz

An AI recently found a counterexample to the Jacobian conjecture.

𝑓(𝑥,𝑦,𝑧)=((1+𝑥𝑦)3𝑧+𝑦2(1+𝑥𝑦)(4+3𝑥𝑦),𝑦+3𝑥(1+𝑥𝑦)2𝑧+3𝑥𝑦2(4+3𝑥𝑦),2𝑥−3𝑥2𝑦−𝑥3𝑧)

I wondered if the counterexample to the Jacobian conjecture could be visualised.
Here's what I came up with:

https://www.desmos.com/3d/cqjyedoauh

The red curve (a simple 3D spiral on the surface of a sphere) is the input of the Jacobian conjecture counterexample, the blue curve is the transformed output.

https://www.desmos.com/calculator/9j9xsrefnb

Im planning on adding more to this like sounds and different pendulum types! The best part about this is that I made it by mistake

Hey guys! I think this is pretty neat.

While reverse engineering Desmos for this project, I ended up getting a pretty good understanding of how it works internally. I've always wanted to define my own "built-in" JavaScript functions in Desmos, and since I also wanted to build my first browser extension, I decided to give it a shot - and I actually managed to do it.

The first time you open the extension, you'll see a few built-in functions like isprime, primefactors, lambertw, and more (see the screenshots). I picked functions that I thought could be somehow useful to people. You can edit, disable, or delete any of them.

You can also create your own functions using the Function Builder Dashboard (see Picture 3). Just enter the body of the function you want to define, reload Desmos, and it'll be available instantly.

It works with both Desmos and Desmodder.

I didn't upload it to the Chrome Web Store because it costs $5 to publish an extension there, so you'll have to install it from GitHub instead (it's really not that difficult, you can find a guide in the GitHub README).

GitHub repository: https://github.com/tobacek/Desmos-Custom-Function-Extension/

If you want to see it in action, here's a Fourier series drawer that uses some of the custom functions:

Demo: https://www.desmos.com/calculator/qe6lyz8tcb

Note: As I said, I'm still very new to this kind of stuff. I tried to make the extension as robust and user-friendly as possible, but Desmos' internal code changes constantly, so I can't guarantee it'll still work a few weeks from now. It'll probably need ongoing maintenance, and I don't know if I'll have enough time to keep up with it in the future.

If anyone more experienced than me wants to help out, I'd really appreciate it (just message me). I also had an AI help clean up and organize the code, so hopefully it's not too painful to work with.

For the function sin(b(ln(x²+y²)))=0 for b€R the geometrical ratio lambda of this function(r_{n+1}/r_{n})=e^{π/2b}.

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So i saw that when n=x box simplifies to box 2 which looks a lot life the taylor series for e^x box 4 so i plugged box 1 into a summation and got this. Anyone know if there is an equation for this cause i think I've seen similar graphs that used the lesser known trig functions. https://www.desmos.com/calculator/qpgo1e4ypd

https://www.desmos.com/3d/r8jr53zimx

Wowie Zowie!!!​

I'm working on a simple project where i have a circle and a point. I've got the circle to have a radius that is the distance from the point has from the origin, so that if the circle is centered on the origin the point will always go through the circle. This point is a draggable. I also have a draggable point that moves the center of the circle and i was wondering if there's a way for the first point to stay on the circle as it moves? i want the first point to be draggable in all four directions but automatically move with the circle if the circle moves. I don't think this is possible but i'm no expert. The following link is hopefully a better visualization of what i mean. Just looking for an answer on whether this is possible, thanks.

https://www.desmos.com/calculator/or9hih66sj

Edit: Solved, thanks (credit to u/4Aethyr)

Made a little 3d (2d desmos) graph to visualize the mandelbrot set in 3d but couldnt figure it out so i got this.

https://www.desmos.com/calculator/wjvxs5sdxl

graph:https://www.desmos.com/calculator/1b24f3d1e3

Yea both are same, but if i put an =x text, how does it become a bernerd graph WHILE THEY'RE THE EXACT SAME!?!?!?

thanks in advance

Link: Keyboard in Desmos

Made with points.

https://www.desmos.com/calculator/17junyoc8z?lang=en next checkpoint on day 23

Bernard has been covered in both ketchup and mustard (probably because of my colour choices)

The Smith chart is an graphical tool used in radio frequency (RF) and microwave engineering to solve complex impedance, transmission line, and matching network problems. Invented by Phillip H. Smith in 1939, it visually maps complex impedance using the function G(z). Inspired by the veratasium video The Scariest Chart in Electricical Engineering and current line of study, (CE major), I was able to make this mainly using lists and parametric curves.

This is a quick experiment I did where you define functions where each point has a perpendicular distance r from the central function. This can give some really messy results ( see sin(1/x) )but in general I thought it was pretty interesting. https://www.desmos.com/geometry/fn38mshzbc